MinT - Best Known (93−57, 93, s)-Nets in Base 25

Best Known (93−57, 93, s)-Nets in Base 25

(93−57, 93, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 93, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 93, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(93−57, 93, 18436)-Net in Base 25 — Upper bound on s

There is no (36, 93, 18437)-net in base 25, because

1 times m-reduction [i] would yield (36, 92, 18437)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 408 102265 260342 767928 833055 905813 652257 374990 070075 120136 442702 120779 087799 508489 129712 929760 198563 217277 958978 725285 153713 887905 > 25⁹² [i]